College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 390: 101

Answer

$ID_1=ID_2 + 1$. $ID_1$ is $1$ more than $ID_2$.

Work Step by Step

$ID=\frac{\log(2A/W)}{\log 2},$ Whereas $W$=width of the target and, $A$=distance to the center of the target. $A=100mm, W_1=5mm$. $ID_1=\frac{\log(2(100)/5)}{\log 2},$ $ID_1=\frac{\log(200/5)}{\log 2},$ $ID_1=\frac{\log40}{\log 2}=\frac{1.6021}{0.3010}=5.322,$ $A=100mm, W_2=10mm$. $ID_2=\frac{\log(2(100)/10)}{\log 2},$ $ID_2=\frac{\log(200/10)}{\log 2},$ $ID_2=\frac{\log20}{\log 2}=\frac{1.3010}{0.3010}=4.322,$ Therefore, $ID_1=ID_2 + 1$. $ID_1$ is $1$ more than $ID_2$.
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